{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from sklearn.model_selection import train_test_split\n",
    "from data import *\n",
    "from evaluation import *\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 加载数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " data length: 100000 \n",
      " user number: 943 \n",
      " item number: 1682\n"
     ]
    }
   ],
   "source": [
    "data_dir = 'datasets/ml-100k/u.data' \n",
    "N, M, data_list, _ = load_data(file_dir=data_dir)\n",
    "print(' data length: %d \\n user number: %d \\n item number: %d' %(len(data_list),N,M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分割数据集"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "train length: 80000 \n",
      " test length: 20000\n"
     ]
    }
   ],
   "source": [
    "train_list, test_list = train_test_split(data_list,test_size=0.2)\n",
    "print ('train length: %d \\n test length: %d' %(len(train_list),len(test_list)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 将 list 转换成 矩阵"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_mat = sequence2mat(sequence = train_list, N = N, M = M)\n",
    "test_mat = sequence2mat(sequence = test_list, N = N, M = M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 参数设置"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.005\n",
    "lamda_regularizer = 0.1\n",
    "max_iteration = 100\n",
    "K = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 非负矩阵分解 （NMF）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " loss:548530.0227,mae:3.5127,rmse:13.6117,recall:0.0210,precision:0.0446\n",
      " step:10 \n",
      " loss:35773.9410,mae:0.7704,rmse:0.9787,recall:0.0350,precision:0.0743\n",
      " step:20 \n",
      " loss:30101.7777,mae:0.7503,rmse:0.9236,recall:0.0396,precision:0.0841\n",
      " step:30 \n",
      " loss:26369.0138,mae:0.7517,rmse:0.9310,recall:0.0408,precision:0.0866\n",
      " step:40 \n",
      " loss:24197.1030,mae:0.7575,rmse:0.9496,recall:0.0398,precision:0.0845\n",
      " step:50 \n",
      " loss:22858.6473,mae:0.7630,rmse:0.9660,recall:0.0389,precision:0.0824\n",
      " step:60 \n",
      " loss:21960.7530,mae:0.7676,rmse:0.9803,recall:0.0355,precision:0.0752\n",
      " step:70 \n",
      " loss:21319.3049,mae:0.7716,rmse:0.9934,recall:0.0335,precision:0.0709\n",
      " step:80 \n",
      " loss:20839.0885,mae:0.7752,rmse:1.0056,recall:0.0315,precision:0.0668\n",
      " step:90 \n",
      " loss:20466.1888,mae:0.7785,rmse:1.0169,recall:0.0299,precision:0.0633\n",
      " end. \n",
      " loss:20195.2326,mae:0.7814,rmse:1.0266,recall:0.0279,precision:0.0593\n",
      "MAE:0.7814;RMSE:1.0266;Recall:0.0279;Precision:0.0593\n"
     ]
    },
    {
     "data": {
      "image/png": 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JOkjS4cAPgOb0ijGAO0kCzzXpWkGzgHOAiyKitPrhdUAbcKWkfSR9FDgNOH+gv9uLKpqZ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\nB49M8ZKpekiEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3e456d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5RCRJKk/bBZHZ02YPWrdHRJKk8rRdEKntETGISJJUnrYLInOmzRm07mBVSZLK03ZBxFsz\nkiS1jrYLIrOmemtGkqRW0XZBZM70mlszPjUjSVJp2i6I2CMiSVLraLsg4hgRSZJaR9sHEZ+akSSp\nPG0fROwRkSSpPAYRg4gkSaUpPYhExMci4taIWBMRqyPivyLi+SPsc2RE9NcsfRGx60jn89aMJEmt\no/QgAhwO/DPwcuBYYBpwZUTMGnYvSGB/YFFlWZyZj450MntEJElqHVPLbkBmvr56PSJOBR4FOoGf\njrD7Y5m5Zizn810zkiS1jlboEam1gKK34w8j1Avg9oh4OCKujIhXjebg27xrxgnNJEkqTUsFkYgI\n4ALgp5l55zBVHwHeC7wFeDPwEHB9RBwy0jnq3ZrJzHG3WZIkjV/pt2ZqfBl4IXDYcJUy8x7gnqqi\nWyJiX2AZcMpw+5779+fC41XHIrlon4s49c9PHWeTJUmaPLq6uujq6hpU1tPTM2Hni1bpDYiIfwHe\nCByemQ+OY//PA4dlZt0QExFLgOVX//Rqjr362EHbVv31KhbOXTiOVkuSNPl1d3fT2dkJ0JmZ3Y08\ndkvcmqmEkDcBR48nhFQcQnHLZli1g1XBAauSJJWl9FszEfFlYClwArAuIga6Jnoyc2OlzqeB52bm\nKZX1M4H7gTuAmcDpwNHAcSOdb8aUGUyJKfRl39Yyg4gkSeUoPYgA76N4Sub6mvLTgIsrf14M7F61\nbTpwLrAbsB5YARyTmTeOdLKIYO70ufRseuZ+l5OaSZJUjtKDSGaOeHsoM0+rWT8HOGe856wNIvaI\nSJJUjpYYI9Js82bMG7RuEJEkqRxtGUTmTp87aN1JzSRJKkdbBpHa2VXX9a4rqSWSJLW3tgwitT0i\n6zYbRCRJKkNbBpE50wf3iDhGRJKkcowpiETEyyJiyjDbZ0TEW7e/WRNr7rSaHhFvzUiSVIqx9ojc\nDOw8sBIRayJin6rtC4CubfZqMfaISJLUGsYaRGKE9aHKWkrtGBGDiCRJ5ZiIMSKt8Ra9YfjUjCRJ\nraEtB6vaIyJJUmsYzxTvL4yIRZU/B/CCiBj4ZH9OY5o1sWrHiPj4riRJ5RhPELmGweNAflD5mZXy\nlr81Y4+IJEmtYaxBZO8JaUWTOUZEkqTWMKYgkpkrR6oTES8ef3Oawx4RSZJaQ0MGq0bEvIh4T0Tc\nCvyiEcecSI4RkSSpNWxXEImIIyLiIuAR4G+Aa4FXNKJhE6m2R2TDlg309feV1BpJktrXmAerVp6Y\nORV4F7ATcCkwA/iTzLyzoa2bILVBBGB973rmzZhXQmskSWpfY33XzPeBu4GXAH8F7JaZfzkRDZtI\ntYNVwXEikiSVYaw9In8EfBH4Smb+ZgLa0xT1ekR8ckaSpOYb6xiRVwPzgOUR8d8R8cGI2CEmMas2\nfcp0ptS8RNgeEUmSmm9MQSQzb8nM04HFwL8CJwMPV45zXETsEIMsImKbXhGfnJEkqfnG9dRMZq7L\nzAsz89XAQcC5wEeBRyPiskY2cKLUPsJrj4gkSc233fOIZObdmXkW8DyKHpKWn+IdnNRMkqRWMKbB\nqhFx4SiqPTHOtjSV07xLklS+sT41cyqwEriNwS++q2aPiCRJGpWxBpGvAEspXn73deBbmfmHhreq\nCZzmXZKk8o31qZkPUDwx83ngjcBDEXFpRLw2IobqIWlJ9ohIklS+MQ9WzcxNmdmVmccBLwTuAL4M\nPBAR284U1qIcIyJJUvm296mZfooxIQFMGaFuS7FHRJKk8o05iETEjIhYGhFXAfdQzCPyQWCPzNxh\nPs3tEZEkqXxjfXz3yxRzhTwEXAgszczHJ6JhE80eEUmSyjfWp2beBzwI3AccCRxZb4xqZr55+5s2\nsXxqRpKk8o01iFzMDjJPyEjsEZEkqXxjCiKZeWqjGxARHwNOBF4AbABuAj6SmfeMsN9RFO+4eRFF\nL80/ZuZFoz2vY0QkSSrfdr9rpgEOB/4ZeDlwLDANuDIiZg21Q0TsBfwAuAY4GPgC8LWIOG60J7VH\nRJKk8o311kzDZebrq9cj4lTgUaAT+OkQu70fuK/ysj2AuyPi1cAy4KrRnLc2iDhGRJKk5muFHpFa\nCyjGoQw3dfwrgKtryq4AXjnak9QOVrVHRJKk5mupIFKZJv4C4KeZeecwVRcBq2vKVgM7RcSM0Zxr\nmx6R3nX0Z/8YWitJkrZX6bdmanyZYtr4wyb6RLWDVQE29G7YpqdEkiRNnJYJIhHxL8DrgcMz85ER\nqq8CFtaULQTWZOam4XZctmwZ8+fPZ3PfZri3UnhQsTy9+WmDiCSprXV1ddHV1TWorKenZ8LOF5nl\nTwtSCSFvAo7MzPtGUf+zwB9l5sFVZZcAC2oHv1ZtXwIsX758OUuWLGF973rmfHpw6Pjth37LPs/a\nZ3v+KpIkTTrd3d10dnYCdGZmdyOPXfoYkcq08W8H3gasi4iFlWVmVZ1PR0T1HCFfBfaJiM9FxAER\ncQZwEnDeaM87a+osgsGzwjpgVZKk5io9iFBMG78TcD3wcNXy1qo6i4HdB1Yy8wHgDRTzjtxO8dju\nuzKz9kmaIUWE07xLklSy0seIZOaIYSgzT6tTdiPFXCPjNnf63EG9IPaISJLUXK3QI1Iap3mXJKlc\nbR1EnOZdkqRytXUQcYyIJEnlausgYo+IJEnlausg4hgRSZLK1dZBxB4RSZLK1dZBZJseEceISJLU\nVG0dRLbpEem1R0SSpGYyiFTx1owkSc3V1kHEx3clSSpXWwcRe0QkSSpXWwcRH9+VJKlcbR1E7BGR\nJKlcbR1EHCMiSVK52jqI2CMiSVK52jqI1BsjkpkltUaSpPbT1kGktkekP/vZuGVjSa2RJKn9tHUQ\nqR0jAj45I0lSM7V1EKntEQHHiUiS1ExtHURmT5u9TZlPzkiS1DxtHUQ6omObMGKPiCRJzdPWQQSc\nXVWSpDK1fRBxLhFJksrT9kGk9skZg4gkSc3T9kGktkfEwaqSJDVP2weR2jEi9ohIktQ8bR9EtukR\ncbCqJElNYxBxsKokSaVp+yCyzeO7jhGRJKlp2j6IbNMj0muPiCRJzdL2QaT28V17RCRJap62DyKO\nEZEkqTxtH0Sc4l2SpPK0RBCJiMMj4rKI+H1E9EfECSPUP7JSr3rpi4hdx3pue0QkSSpPSwQRYA5w\nO3AGkKPcJ4H9gUWVZXFmPjrmEztGRJKk0kwtuwEAmXk5cDlARMQYdn0sM9dsz7ntEZEkqTyt0iMy\nHgHcHhEPR8SVEfGq8RzEMSKSJJVnRw0ijwDvBd4CvBl4CLg+Ig4Z64Hq9YhkjvbukCRJ2h4tcWtm\nrDLzHuCeqqJbImJfYBlwyliOVTtGZEv/Fjb3bWbG1Bnb3U5JkjS8HTKIDOFW4LCRKi1btoz58+dv\nXd+4ZSPMBg56ps663nUGEUlSW+rq6qKrq2tQWU9Pz4SdL1rtNkRE9AN/kpmXjXG/K4E1mXnSENuX\nAMuXL1/OkiVLtpb3bOxhwecWDKq78q9Wssf8PcbcdkmSJqPu7m46OzsBOjOzu5HHbokekYiYA+xH\nMQAVYJ+IOBj4Q2Y+FBGfAXbLzFMq9c8E7gfuAGYCpwNHA8eN9dy1t2bAR3glSWqWlggiwKHAdRRz\ngyRwbqX8IuCdFPOE7F5Vf3qlzm7AemAFcExm3jjWE0/tmMqMKTPY1Ldpa5mP8EqS1BwtEUQy8waG\neYInM0+rWT8HOKdR5587fS6bNjwTRHyEV5Kk5thRH99tqNrbM/aISJLUHAYRtp1LxDEikiQ1h0EE\np3mXJKksBhGc5l2SpLIYRLBHRJKkshhE2HawqmNEJElqDoMIMHeaPSKSJJXBIEKdHhHHiEiS1BQG\nERwjIklSWQwibPvUjEFEkqTmMIhQZ0Izb81IktQUBhGc4l2SpLIYRHCKd0mSymIQwTEikiSVxSCC\nY0QkSSqLQQTHiEiSVBaDCDB/xvxB65v7NvP4+sdLao0kSe3DIALs/ay9mTl15qCy21fdXlJrJElq\nHwYRYGrHVA7a9aBBZbc9cltJrZEkqX0YRCpeuuilg9ZvW2UQkSRpohlEKl662CAiSVKzGUQqantE\n7n78bic2kyRpghlEKg5aeBAd8czlSJIVq1eU2CJJkiY/g0jF7GmzecFzXjCozNszkiRNLINIlW0G\nrPrkjCRJE8ogUsUnZyRJai6DSJXaJ2d++egv6e3rLak1kiRNfgaRKocsOmTQ+ua+zdz1+F0ltUaS\npMnPIFLl2bOezZ7z9xxU5jgRSZImjkGkhhObSZLUPAaRGg5YlSSpeQwiNWrHidy+6nb6s7+k1kiS\nNLkZRGrU9ois2bSG+5+8v6TWSJI0uRlEajxvp+ex86ydB5V5e0aSpInREkEkIg6PiMsi4vcR0R8R\nJ4xin6MiYnlEbIyIeyLilAa1ZdsBqz45I0nShGiJIALMAW4HzgBypMoRsRfwA+Aa4GDgC8DXIuK4\nRjTGAauSJDXH1LIbAJCZlwOXA0REjGKX9wP3ZeZZlfW7I+LVwDLgqu1tj0FEkqTmaJUekbF6BXB1\nTdkVwCsbcfDaWzOrnl7FqqdXNeLQkiSpyo4aRBYBq2vKVgM7RcSM7T34/s/en9nTZg8qu33V7dt7\nWEmSVKMlbs0007Jly5g/f/6gsqVLl7J06dKt61M6pnDwwoO5+Xc3by277ZHbeN1+r2taOyVJKkNX\nVxddXV2Dynp6eibsfDtqEFkFLKwpWwisycxNw+14/vnns2TJkhFP8NJFLx0URC751SV85NUfoSN2\n1E4kSZJGVvvlHKC7u5vOzs4JOd+O+ql6M3BMTdnxlfKGOH7f4wet/+rRX/HdO7/bqMNLkiRaJIhE\nxJyIODgiBuZX36e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      "text/plain": [
       "<matplotlib.figure.Figure at 0x9c47c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from nmf import *\n",
    "model = nmf_sgd(train_list=train_list, \n",
    "                test_list=test_list, \n",
    "                N=N, \n",
    "                M=M,\n",
    "                K=K,\n",
    "                learning_rate=learning_rate,\n",
    "                max_iteration=max_iteration)\n",
    "P, Q, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1],records_array[:,4][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,0],name='loss')\n",
    "figure(values_list=records_array[:,1],name='MAE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " loss:8707493.4678,mae:3.9447,rmse:84.1428,recall:0.0246,precision:0.0522\n",
      " step:10 \n",
      " loss:3199449.5738,mae:3.3928,rmse:13.5287,recall:0.0186,precision:0.0393\n",
      " step:20 \n",
      " loss:8554693.1306,mae:3.8606,rmse:156.5868,recall:0.0221,precision:0.0470\n",
      " step:30 \n",
      " loss:2260663.8981,mae:3.5777,rmse:23.9332,recall:0.0288,precision:0.0611\n",
      " step:40 \n",
      " loss:1444433.1167,mae:3.5569,rmse:16.6414,recall:0.0246,precision:0.0522\n",
      " step:50 \n",
      " loss:1481557.5129,mae:3.6021,rmse:19.0156,recall:0.0260,precision:0.0551\n",
      " step:60 \n",
      " loss:1197875.3457,mae:3.5201,rmse:13.8019,recall:0.0268,precision:0.0568\n",
      " step:70 \n",
      " loss:664191712470.3215,mae:129.1503,rmse:8327084.0316,recall:0.0181,precision:0.0384\n",
      " step:80 \n",
      " loss:11659071.4916,mae:3.6568,rmse:38.6617,recall:0.0264,precision:0.0560\n",
      " step:90 \n",
      " loss:497986817.2438,mae:5.7873,rmse:4052.4777,recall:0.0251,precision:0.0532\n",
      " end. \n",
      " loss:16765422.3427,mae:3.7906,rmse:128.3636,recall:0.0181,precision:0.0383\n",
      "MAE:3.7906;RMSE:128.3636;Recall:0.0181;Precision:0.0383\n"
     ]
    },
    {
     "data": {
      "image/png": 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oDCJqLJfvSpM9tPEh7txw54Sym0durqg1kkFEDTaXnVVdvqtBcdeGu2ZVJvWL\nQUSNNacekbRHRIPBIKK6MYiokTJz0koY9xGRDCKqH4OIGmksxyaVOUdEYtL8EIA7H5xcJvWLQUSN\n1ClYuMW7NEWPyEP2iKg6BhE1UqcNyly+Kzk0o/oxiKiRZuoRMYhoUBlEVDcGETXSXIOIW7xrUBhE\nVDe1CSIRcVxE3BgRD0XEDyPit6apu19EjLXdRiNih362WfU14xyRxW7xrsHUabLq3Rvu7jjBW+qH\nWgSRiHgtcDLwQeC5wOXAWRGx3TSHJfAMYMfytlNm3tHrtmph6DT51OW7Uufej9Ec5b6H76ugNVJN\nggiwBvjbzPxyZl4DvB3YALxphuPuzMw7xm89b6UWDOeISJ1NNQzj8IyqUnkQiYilwGrg3PGyzEzg\nHOCF0x0KXBYRt0bE2RHxot62VAuJy3elyTLTIKLaqTyIANsBi4H1beXrKYZcOrkNeBtwJPBq4Bbg\n+xGxd68aqYWl0+RTe0Q06EYeGZnyd91NzVSVJTNXqZ/MvA64rqXohxHxdIohnqOnO3bNmjWsWLFi\nQtnQ0BBDQ0Ndb6eq0/5muygWsSieyN0GEQ2i6Xo97BHRuOHhYYaHhyeUjYyM9Oz16hBE7gJGgZVt\n5SuB2+fwPJcAL56p0tq1a1m1atUcnlYL0XQXvOt03+W7GgQGEc1Gpw/n69atY/Xq1T15vcqHZjJz\nI3ApcOB4WUREef+iOTzV3hRDNtKMQcTluxpEBhHVUR16RABOAb4YEZdS9GysAZYDXwSIiBOBnTPz\n6PL+u4EbgSuBZcBbgQOAg/vectVS++TT9smpDs1oEE03D6TT/iJSP9QiiGTmN8o9Qz5MMSRzGfDy\nzBz/y9gR2KXlkM0o9h3ZmWKZ7xXAgZl5Qf9arTqb69CMQUSDwB4R1VEtgghAZp4KnDrFY8e03T8J\nOKkf7dLCNOc5Ii7f1QAwiKiOKp8jIvVCexBpnxPSPlRjj4gGgUFEdWQQUSO1r4JxaEaCux4yiKh+\nDCJqJJfvSpNNN1l15JERHh19tI+tkQoGETWSy3elyWbq9bh7w919aon0BIOIGsnlu9JkMwURh2dU\nBYOIGmmuQzNjOcZYjvW8XVJVHht7jHsfvnfaOgYRVcEgokaaaxDpdIzUJJ2GXVZsPvG6W25qpioY\nRNRIc12+2+kYqUk69Xbssd0eM9aRes0gokaa6/JdMIio2dpDxjbLtmGnJ+00bR2pHwwiaiSHZqSJ\n2kPGdsscA2UGAAAOOUlEQVS3Y7vl201bR+oHg4gaaa7Ld8Ft3tVsBhHVlUFEjTTX5btgj4iarX0i\n6vbLt2f75dtPW0fqB4OIGsmhGWkie0RUVwYRNdJ8gojbvKvJDCKqK4OIGsnlu9JEsw0imdnPZkkG\nETXTTMt3F8XkX32DiJqsff5HpyDy8GMP8+DGB/vZLMkgomaaaWgmIrzejAZKe4/I9su3Z/stt5+x\nntRrBhE10qQgEpPnhLQHEZfvqsk6Dc1stdlWk4YpDSLqN4OIGmnS8t0O+4a0vwHbI6Km2rBxAxs2\nbphQtt3y7YgIJ6yqcgYRNdJMQzOdygwiaqpOF7wbDyDtQeTOB91LRP1lEFEjzSeIuHxXTdU+UXVx\nLGabZdsATJonYo+I+s0gokZ6LNuW73ZYrts+XGOPiJqq0/yQiHj86+nqSr1mEFEjtc8RcWhGg6xT\nEHn86y0MIqqWQUSN5BwR6QnTBpH2HpGHDCLqL4OIGmlec0RcvquGap+A2jovpH2OiJNV1W8GETVS\n+8RTl+9qkE3qEdlimh4Rh2bUZwYRNZJDM9IT2odbph2aMYiozwwiaiSDiPSEucwRufuhuxnLsb60\nSwKDiBrKfUSkJ0y6zkzrHJHlE+eIjOUY9z50b1/aJYFBRA01aYt39xHRAGufgNraC7Lt8m0n1Xd4\nRv1kEFEjOTQjFTJz2qGZZUuW8aTNnjThcYOI+skgokZy+a5UGHlkhNEcnVDWPi/ECauqkkFEjeTy\nXanQKVS0B4/2eSIGEfVTbYJIRBwXETdGxEMR8cOI+K0Z6u8fEZdGxMMRcV1EHN2vtmr2hoeHK3nd\nQR6aqeqcD7I6n/P2+SHLly5n+dLlE8omXYF3Q/03NavzOdfc1CKIRMRrgZOBDwLPBS4HzoqI7aao\nvyvwbeBcYC/gY8DnIuLgfrRXs2cQ6T/foPuvzud8uvkhU5UthB6ROp9zzU0tggiwBvjbzPxyZl4D\nvB3YALxpivrvAG7IzOMz89rM/BRwWvk8kst3pVJTg4iaY/K7c59FxFJgNfCR8bLMzIg4B3jhFIe9\nADinrewsYO1Mr3fiv5/I9rdNHA/NzKnaVvxLzPS0kySdn3PSa8zzuTPz8X/HNx+KCIKY8O982jCW\nYxNvjE2qO/78i2LR47dOrlh/Bcd+59g5f4/zOS+jOcqvHv0VI4+M8Mv7fznhsdks3/3OT7/D3Rvu\n7vjcs/15dtL+vWzKc8303AA/Wf8TjvvOcXN6nl7/vs7WfJ5/uteb6m97ytef4m9mpveI9nM+/rfZ\n3h5o+Rua5d/nbE117i5ff/mE++3zQTqVnf/z8yf83Xbj5zJfU/3+dHpvqbKdnSTF+/Po2CijOcpY\njpEki2Mxi2LR4/+2v3/O9vdnNt/veBvG/68Yf75FsYigeA+f7nfx5ENOZoulW8zp+56ryoMIsB2w\nGFjfVr4e2GOKY3acov7WEbF5Zj4y1YuddtVpcN98m6o5uw8+/aNPV92KWfWIrLttHetuW9evJvXO\nfXDqj06tuhWDZQGd89n0iNx03021+LudVk3eW5ruxANPHIgg0i/LALDHsb8eBm6tuhFw18/uYt3I\nxJDx0M8fqkXbuq4m53ygLKRzvi2sWzfxb+HBnz+4cNo/biGd8wXssh9fxlabb8XVV189XrSs268R\nc+267HoDiqGZDcCRmXl6S/kXgRWZ+aoOx5wPXJqZf9hS9kZgbWY+eYrX+T3gq91tvSRJA+X1mfkP\n3XzCyntEMnNjRFwKHAicDhDFgNWBwMenOOxi4NC2skPK8qmcBbweuIkiS0uSpNlZBuxK8X9pV1Xe\nIwIQEa8BvkixWuYSitUvRwHPysw7I+JEYOfMPLqsvyvwE+BU4PMUoeWjwGGZ2T6JVZIk1VTlPSIA\nmfmNcs+QDwMrgcuAl2fm+K46OwK7tNS/KSIOp1gl8y7gF8CbDSGSJC0stegRkSRJg6kuG5pJkqQB\nZBCRJEmVGYggMtcL6mn2IuI9EXFJRNwfEesj4psR8cwO9T4cEbdGxIaI+G5E7F5Fe5smIk6IiLGI\nOKWt3PPdZRGxc0R8JSLuKs/r5RGxqq2O571LImJRRPxZRNxQns/rI+J9Hep5zucpIvaNiNMj4pfl\n+8gRHepMe34jYvOI+FT5d/FARJwWETvMpR2NDyJzvaCe5mxf4BPA84GDgKXA2RHx+FZ8EfF/gHcC\n/wvYB3iQ4mewWf+b2xxloP5fFL/TreWe7y6LiG2AHwCPAC8H9gT+CLi3pY7nvbtOAN4GHAs8Czge\nOD4i3jlewXO+ybakWBxyLEzeS3+W5/ejwOHAkcBLgZ2Bf5pTKzKz0Tfgh8DHWu4HxSqb46tuWxNv\nFFv2jwEvaSm7FVjTcn9r4CHgNVW3d6HegCcB1wIvA84DTvF89/R8/yVw/gx1PO/dPednAJ9tKzsN\n+LLnvCfneww4oq1s2vNb3n8EeFVLnT3K59pntq/d6B6RlgvqnTtelsWZmu6Ceto021Ak63sAIuJp\nFMuvW38G9wP/gT+DTfEp4IzM/F5roee7Z34H+FFEfKMcglwXEW8Zf9Dz3hMXAQdGxDMAImIv4MXA\nv5b3Pec9NMvz+zyKbUBa61wL3Mwcfga12Eekh+ZzQT3NU7kj7keBCzPzqrJ4R4pg0ulnsGMfm9cY\nEfE6YG+KN4F2nu/e2A14B8Uw719QdFN/PCIeycyv4Hnvhb+k+MR9TUSMUkwleG9mfq183HPeW7M5\nvyuBR8uAMlWdGTU9iKi/TgWeTfGpRT0QEb9GEfYOysyNVbdngCwCLsnM95f3L4+I51DsBv2V6prV\naK8Ffg94HXAVRfj+WETcWoY/NUSjh2YorrU7SpHaWq0Ebu9/c5orIj4JHAbsn5m3tTx0O8W8HH8G\n3bEa2B5YFxEbI2IjsB/w7oh4lOKTiOe7+24Drm4ruxp4avm1v+fd99fAX2bmP2bmlZn5VYrdtN9T\nPu45763ZnN/bgc0iYutp6syo0UGk/MQ4fkE9YMIF9S6qql1NU4aQVwIHZObNrY9l5o0Uv5CtP4Ot\nKVbZ+DOYu3OA36T4dLhXefsR8PfAXpl5A57vXvgBk4dz9wB+Dv6e98hyig+SrcYo/9/ynPfWLM/v\npcBjbXX2oAjo012EdoJBGJo5BfhieYXf8QvqLae4yJ42UUScCgwBRwAPRsR4eh7JzPGrHH8UeF9E\nXE9x9eM/o1i59K0+N3fBy8wHKbqpHxcRDwJ3Z+b4J3bPd/etBX4QEe8BvkHxZvwW4K0tdTzv3XUG\nxfn8BXAlsIri/ftzLXU855sgIrYEdqfo+QDYrZwUfE9m3sIM5zcz74+I/wecEhH3Ag8AHwd+kJmX\nzLohVS8Z6tOypGPLk/gQRUp7XtVtasqN4hPKaIfb77fV+1OKpWAbKC4jvXvVbW/KDfgeLct3Pd89\nO8+HAVeU5/RK4E0d6njeu3e+t6T4IHkjxf4VPwU+BCzxnHftHO83xXv452d7foHNKfaSuqsMIv8I\n7DCXdnjRO0mSVJlGzxGRJEn1ZhCRJEmVMYhIkqTKGEQkSVJlDCKSJKkyBhFJklQZg4gkSaqMQUSS\nJFXGICKptiLixoh4V9XtkNQ7BhFJAETEFyLin8uvz4uIU/r42keX16po9zzg7/rVDkn9NwgXvZNU\nkYhYmsVVsGesCky63kRm3t39VkmqE3tEJE0QEV+guBjWuyNiLCJGI+Kp5WPPiYh/jYgHIuL2iPhy\nRGzbcux5EfGJiFgbEXcCZ5blayLiioj4VUTcHBGfiojl5WP7AZ8HVrS83gfKxyYMzUTELhHxrfL1\nRyLi6xGxQ8vjH4yIH0fEG8pj74uI4fIqo+N1jirbsiEi7oqIsyNii56eVElTMohIavcuiqtUfxZY\nCewE3BIRK4BzgUspLsn+cmAH4Bttx/8+8AjwIuDtZdko8AfAs8vHDwD+unzsIuB/A/e3vN7ftDcq\nIgI4HdgG2Bc4CNgN+Fpb1acDr6S4Wu7hFKHqhPI5dgT+geJS8s8qH/tnnrgMuqQ+c2hG0gSZ+UBE\nPApsyMw7x8sj4p3Ausx8f0vZW4CbI2L3zLy+LP5pZp7Q9pwfb7l7c0S8H/g08M7M3BgRI0W1J16v\ng4OA3wB2zcxby9f/feDKiFidmZeONws4OjM3lHW+AhwIvJ8i5CwGvpmZt5T1r5ztuZHUffaISJqt\nvYCXlcMiD0TEA8DVFHM7nt5S79L2AyPioIg4JyJ+ERH3A18Bto2IZXN4/WcBt4yHEIDMvBq4D9iz\npd5N4yGkdBtFzw3A5RS9Ov8VEd+IiLdExDZzaIOkLjOISJqtJ1EMjfx3ilAyfnsGcEFLvQdbD4qI\nXwfOAC4DXk0xrHNc+fBmPWhn++TYpHyvy8yxzDwEeAVFT8gfANeUbZRUAYOIpE4epRjCaLWOYmjk\n55l5Q9vtoWmeazUQmfnHmXlJOYTzlFm8XrurgV0i4vFjI+LZFHNG5jS8kpkXZ+aHgOdSBJdXzeV4\nSd1jEJHUyU3A8yPi11tWxXwK+G/A1yLieRGxW0S8PCI+X04kncr1wNKIeFdEPC0i/ifwtg6v96SI\neFlEbNtpFUtmngP8F/DViHhuROwDfAk4LzN/PJtvKiL2iYj3RMTqiNgFOBLYDrhqNsdL6j6DiKRO\n/oZipctVwB0R8dTMvA14McX7xlnAFcApwL2ZOb4HSKe9QK4A/hA4HvgJMES5iqWlzsXAZ4CvA3cA\nfzLF8x0B3AucD5xNEXJeN4fv637gpcB3gGuBDwN/mJlnz+E5JHVRPPH+IUmS1F/2iEiSpMoYRCRJ\nUmUMIpIkqTIGEUmSVBmDiCRJqoxBRJIkVcYgIkmSKmMQkSRJlTGISJKkyhhEJElSZQwikiSpMgYR\nSZJUmf8PAUJDp8e/IUoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x95ea160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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96QL8GlJC9G1RJKBwIlEUlZ6TrMxse2AG8FB/mbuvA54CPhIW7UUQtFLrvAy8kVJHZICG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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb484c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = nmf_mult(train_list=train_list, \n",
    "                 test_list=test_list, \n",
    "                 N=N, \n",
    "                 M=M,\n",
    "                 K=K,\n",
    "                 max_iteration=max_iteration)\n",
    "P, Q, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1],records_array[:,4][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,0],name='loss')\n",
    "figure(values_list=records_array[:,1],name='MAE')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(514032.52780216181, 2.366875907452588, 6.9482022067689044, 0.15175, 0.32184517497348886)\n"
     ]
    }
   ],
   "source": [
    "# sklearn 自带的 NMF 算法\n",
    "from sklearn.decomposition import NMF\n",
    "model = NMF(n_components=10, init='random', random_state=0)\n",
    "train_mat = sequence2mat(sequence = train_list, N = N, M = M)\n",
    "W = model.fit_transform(train_mat)\n",
    "H = model.components_\n",
    "\n",
    "def prediction(P, Q):\n",
    "    N,K = P.shape\n",
    "    M,K = Q.shape\n",
    "\n",
    "    rating_list=[]\n",
    "    for u in range(N):\n",
    "        u_rating = np.sum(P[u,:]*Q, axis=1)\n",
    "        rating_list.append(u_rating)\n",
    "    r_pred = np.array(rating_list)\n",
    "    return r_pred\n",
    "\n",
    "# 预测评分\n",
    "user = np.array(train_list)[:,0].astype(np.int16)\n",
    "item = np.array(train_list)[:,1].astype(np.int16)\n",
    "rating_true = np.array(train_list)[:,2]\n",
    "rating_pred = np.sum(W[user,:]*H.T[item,:],axis=1)\n",
    "loss = np.sum((rating_true-rating_pred)**2)\n",
    "pred_mat = prediction(W, H.T)\n",
    "\n",
    "# 评估算法\n",
    "mae, rmse, recall, precision = evaluation(pred_mat, train_mat, test_mat)\n",
    "print(loss, mae, rmse, recall, precision)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 矩阵分解 （MF，SVD，Funk-SVD）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " loss:549274.8142,mae:3.5114,rmse:13.5999,recall:0.0180,precision:0.0382\n",
      " step:10 \n",
      " loss:65404.5762,mae:0.7808,rmse:0.9881,recall:0.0328,precision:0.0697\n",
      " step:20 \n",
      " loss:62533.4391,mae:0.7558,rmse:0.9159,recall:0.0324,precision:0.0687\n",
      " step:30 \n",
      " loss:61332.1955,mae:0.7446,rmse:0.8871,recall:0.0362,precision:0.0767\n",
      " step:40 \n",
      " loss:60545.2057,mae:0.7383,rmse:0.8724,recall:0.0366,precision:0.0776\n",
      " step:50 \n",
      " loss:59904.4783,mae:0.7340,rmse:0.8630,recall:0.0352,precision:0.0747\n",
      " step:60 \n",
      " loss:59376.8684,mae:0.7311,rmse:0.8572,recall:0.0340,precision:0.0721\n",
      " step:70 \n",
      " loss:58962.1662,mae:0.7294,rmse:0.8539,recall:0.0315,precision:0.0668\n",
      " step:80 \n",
      " loss:58647.0056,mae:0.7284,rmse:0.8525,recall:0.0302,precision:0.0642\n",
      " step:90 \n",
      " loss:58408.7568,mae:0.7279,rmse:0.8522,recall:0.0285,precision:0.0606\n",
      " end. \n",
      " loss:58242.9217,mae:0.7278,rmse:0.8523,recall:0.0278,precision:0.0591\n",
      "MAE:0.7278;RMSE:0.8523;Recall:0.0278;Precision:0.0591\n"
     ]
    },
    {
     "data": {
      "image/png": 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rg1Ap5TVj2ZFe5IiQJEnNGulkaY2CHSd61ZgkSU0yCDXIESFJkpplEGqQQUiS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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa036c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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cmpEkqTxtF0Tmz5k/Yt2hGUmSytN2QWRh58IR6w7NSJJUnrYLIvaISJLUOto+iDhHRJKk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\nmSx4icfFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb37ac50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from mf import *\n",
    "model = mf(train_list=train_list, \n",
    "           test_list=test_list, \n",
    "           N=N, \n",
    "           M=M,\n",
    "           K=K,\n",
    "           learning_rate=learning_rate, \n",
    "           lamda_regularizer=lamda_regularizer, \n",
    "           max_iteration=max_iteration)\n",
    "P, Q, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1],records_array[:,4][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,0],name='loss')\n",
    "figure(values_list=records_array[:,1],name='MAE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 概率矩阵分解 （PMF）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " loss:549680.3605,mae:3.5177,rmse:13.6469,recall:0.0159,precision:0.0337\n",
      " step:10 \n",
      " loss:65535.5941,mae:0.7818,rmse:0.9908,recall:0.0328,precision:0.0695\n",
      " step:20 \n",
      " loss:62663.5601,mae:0.7575,rmse:0.9199,recall:0.0320,precision:0.0679\n",
      " step:30 \n",
      " loss:61381.9854,mae:0.7450,rmse:0.8886,recall:0.0357,precision:0.0756\n",
      " step:40 \n",
      " loss:60529.2566,mae:0.7377,rmse:0.8716,recall:0.0365,precision:0.0773\n",
      " step:50 \n",
      " loss:59862.3450,mae:0.7332,rmse:0.8611,recall:0.0359,precision:0.0761\n",
      " step:60 \n",
      " loss:59330.9171,mae:0.7303,rmse:0.8550,recall:0.0342,precision:0.0725\n",
      " step:70 \n",
      " loss:58917.3884,mae:0.7287,rmse:0.8520,recall:0.0316,precision:0.0670\n",
      " step:80 \n",
      " loss:58603.5406,mae:0.7280,rmse:0.8509,recall:0.0298,precision:0.0632\n",
      " step:90 \n",
      " loss:58368.0323,mae:0.7278,rmse:0.8511,recall:0.0280,precision:0.0594\n",
      " end. \n",
      " loss:58206.2076,mae:0.7279,rmse:0.8517,recall:0.0271,precision:0.0575\n",
      "MAE:0.7279;RMSE:0.8517;Recall:0.0271;Precision:0.0575\n"
     ]
    },
    {
     "data": {
      "image/png": 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1ffmYmZmZDYHCg5Ckf5E0XdIOkj4I3AC0Ar9IS84HTpf0CUm7A1cALwA3wobJ05cC50k6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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a8a6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa036dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pmf import *\n",
    "model = pmf(train_list=train_list, \n",
    "            test_list=test_list, \n",
    "            N=N, \n",
    "            M=M,\n",
    "            K=K,\n",
    "            learning_rate=learning_rate, \n",
    "            lamda_regularizer=lamda_regularizer, \n",
    "            max_iteration=max_iteration)\n",
    "P, Q, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1],records_array[:,4][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,0],name='loss')\n",
    "figure(values_list=records_array[:,1],name='MAE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4. 权重矩阵分解 （WMF）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " mae:2.1109,rmse:6.8433,recall:0.0176,precision:0.0374\n",
      " step:1 \n",
      " mae:0.8642,rmse:1.2853,recall:0.0694,precision:0.1472\n",
      " step:2 \n",
      " mae:0.8465,rmse:1.2464,recall:0.0757,precision:0.1607\n",
      " step:3 \n",
      " mae:0.8374,rmse:1.2206,recall:0.0779,precision:0.1652\n",
      " step:4 \n",
      " mae:0.8316,rmse:1.2020,recall:0.0775,precision:0.1645\n",
      " step:5 \n",
      " mae:0.8281,rmse:1.1907,recall:0.0779,precision:0.1651\n",
      " step:6 \n",
      " mae:0.8264,rmse:1.1850,recall:0.0779,precision:0.1652\n",
      " step:7 \n",
      " mae:0.8255,rmse:1.1826,recall:0.0789,precision:0.1673\n",
      " step:8 \n",
      " mae:0.8250,rmse:1.1822,recall:0.0779,precision:0.1651\n",
      " step:9 \n",
      " mae:0.8248,rmse:1.1828,recall:0.0780,precision:0.1655\n",
      " end. \n",
      " mae:0.8248,rmse:1.1828,recall:0.0780,precision:0.1655\n",
      "MAE:0.8248;RMSE:1.1828;Recall:0.0780;Precision:0.1655\n"
     ]
    },
    {
     "data": {
      "image/png": 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55mPU4FE7g0Z3L5M1M7PK4iBimWva1sSVf7mS+Qvns3XH1qJ9Xr/767n4LRdz7F7HVv1l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\nZpYZBxEzMzPLjIOImZmZZeb/B3agl/Zrqe8OAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa229160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9nIrn9UPMzKzWVUQQAYiIhcDCIu+dV6Ct0zt+IuI1ZSotE23Rxj0r7slp8/wQ\nMzOrNZVw+64V8NS6p9i4Y2NOm4OImZnVGgeRCrVoxaKc7eljpjNldP7olJmZWXVzEKlQ+RNV506b\nm1ElZmZmfcdBpAJFhBcyMzOzAcFBpAI9u+FZ1m7NXfHeQcTMzGqRg0gFyr8actCog3jtAa/NqBoz\nM7O+U/Ltu5LqgMOACeQFmoi4u+BO1i35E1VPm3YayWKzZmZmtaWkICLpROCHwDSS1U07CpKn6VqJ\nPFHVzMwGilKviNwEPAy8HXiJV1c4tV5a8coKVraszGnz/BAzM6tVpQaR1wHviog/lrMY2/dqyIHD\nD+SI8UdkVI2ZmVnfKnWy6kMk80OszPKDyKnTTqVOnlNsZma1qdQrIjcA10qaBDwB7O74ZkQ83tvC\nBqp9Jqr6QXdmZlbDSg0iP03//F6HtiCZuOrJqiV6afNLPLvh2Zy2udM9UdXMzGpXqUGkqp9sW6nu\nWZn7tN39huzH0ROPzqgaMzOzvldSEImIFeUuxPadHzJn6hzq63xxyczMaldvFjR7LfBZoP2WjqXA\ndRHxp3IUNhD5+TJmZjbQlHQ7hqQzSYLH8cDj6esE4ClJbylfeQPHhu0beGLdEzltDiJmZlbrSr0i\n8nVgQUR8sWOjpK8D1wC/7m1hA809K3LnhwwfNJxjJx+bUTVmZmb9o9QFKo4A/rVA+/eAI0svZ+DK\nH5Y5acpJDKkfklE1ZmZm/aPUINIMvKlA+5uAdaWXM3DdvTJvfojXDzEzswGg1KGZ7wD/IulQ4P60\n7RTgC8D8chQ2kGzeuZmml5py2jw/xMzMBoJSg8iVwGbg88DVaduLwOXA9b0va2C5f9X9tEXb3u3B\ndYM54ZATMqzIzMysf5S6jkgAC4AFkvZL2zaXs7CBJH9Z9+MPPp4Rg0dkVI2ZmVn/KXkdkXYOIL3n\n9UPMzGyg6nYQkdQEnBERGyU9QvJMmYIiYlY5ihsItu/ezuLVi3PaHETMzGyg6MkVkf8GdqZf/78+\nqGVAemj1Q+xue/XhxXWq4+QpJ2dYkZmZWf/pdhCJiK8V+tp6J39Y5phJx7D/0P0zqsbMzKx/lbrE\n+xRJh3TYPl7StyV9rHylDQz5E1XnTpubUSVmZmb9r9QFzX4IvBlA0iTgLpLnzlwl6aulHFDShZKe\nl7Rd0oOSjuuk7yRJP5D0jKRWSQXXLpH0t5KeTo/5mKSzSqmtr+xq3cUDqx7IafP8EDMzG0hKDSIz\ngfYZln/7AA19AAAe5klEQVQHPBERJwPvAz7U04NJejdwLXAZcAzwGHCnpHFFdhlKsoLrlcCjRY55\nMklg+g7Jiq//Dfw/SRWzBP2SF5ewfc/2nLY5U+dkVI2ZmVn/KzWIDObViat/DtyRfr0MOKiE480D\nbo6IWyNiGXABsA04v1DniFgREfMi4jZgU5Fjfgb4RUTMj4hnIuKrQBPwqRLq6xP580NmTpjJgSMO\nzKgaMzOz/ldqEHkKuEDSqcBbgF+m7ZOBl3tyIEmDgdnAb9rb0gXT7gJOKrE+0n3vymu7s5fHLCs/\nX8bMzAa6UoPIF4CPA78DGiPisbT9r3h1yKa7xgH1wNq89rXApBLrI9233Mcsm9a2Vu5deW9O29zp\nnqhqZmYDS6lLvP8unb+xf0Rs7PDWv5AMqVgXHlv7GJt25o4qnTr11IyqMTMzy0bJS7xHRCuwMa9t\neQmHWg+0AhPz2icCa0oqLrGm1GPOmzeP0aNH57Q1NDTQ0NDQi3Jy5c8Ped3Y13HQfqVMrzEzM+tf\njY2NNDY25rS1tLSUdKzMl3iPiN2SlgBnkE56laR0uzdP8n2gwDHekrZ3asGCBcya1ber1Pv5MmZm\nVq0K/XLe1NTE7Nmze3ysSlnifT5wSxpIFpPcRTMCuAVA0tXA5Ig4t30HSUcDAkYB49PtXRHxdNrl\nOuB3kj4H/C/QQDIp9qNlrr3HIsJBxMzMjApZ4j0ibk/nnFxBMnzyKHBmRDSnXSYBU/J263hVZhbw\nXmAFcGh6zAckvRe4Kn09C5wdEUvLWXspljYv5eXtuTcXeUVVMzMbiEqaI5KueloXEQ/ltZ8AtEbE\nwz09ZkQsBBYWee+8Am1d3vETET8FftrTWvpa/tWQqaOnMm3MtIyqMTMzy06pt+/eSLJmSL6D0/es\nE/usH+JhGTMzG6BKDSJHUnhp9UfS96yIgvNDvJCZmZkNUKUGkZ0UXhjsIGBP6eXUvuc2PseLm1/M\nafMVETMzG6hKDSK/Aq6WtHexDUljgH8Efl2OwmrVohWLcrYnjpzI6w98fUbVmJmZZavUBc0uBu4G\nVqRrikDyhNu1wAfKUVitKnTbbrJsipmZ2cBT6hLvqyW9EXgfcDSwHfg+yXNndpexvprj9UPMzMxe\n1Zsl3reSPFvGumlVyyqef+X5nDYHETMzG8hKnSOCpA9IulfSi5KmpW3zJJ1dvvJqyz0r78nZPmDY\nAcycMDOjaszMzLJXUhCR9AmSZdl/ARwA1KdvbQQ+W57Sas+i5bkTVU+ddip1KjkLmpmZVb1Sfwp+\nGvhoRFxF7u26DwNH9bqqGrXPQmZeP8TMzAa4UoPIa0gWL8u3ExhZejm1a93WdSxbvyynzfNDzMxs\noCs1iDxPcrtuvr8Ani7QPuDdsyJ3fsjIwSM55qBjMqrGzMysMpR618x84EZJwwABx0tqAC4FPlKu\n4mpJ/m27p0w9hUF1Jd+0ZGZmVhNKXUfku5K2A/8AjAB+CLwIXBQRPypjfTUjf0XVudPmZlSJmZlZ\n5ehxEFGyDOgU4KcR8QNJI4BREbGu7NXViI3bN/L42sdz2jw/xMzMrLQ5IgL+SBJGiIhtDiGdu2/V\nfQSxd3to/VCOm3xchhWZmZlVhh4HkYhoA54FDix/ObUpf37IiYecyNBBQzOqxszMrHKUetfMF4Fv\nSvKyoN3g58uYmZkVVuptG7eSTFJ9TNIukofe7RURY3tbWK3YsmsLD7/4cE6bJ6qamZklSg0iXsa9\nmx5Y9QCt0bp3e1DdIE485MQMKzIzM6scPQoikuqAi4GzgSHAb4CvRcT2TnccwPKHZY6dfCwjh3jx\nWTMzM+j5HJG/B/4R2AysBi4Cbix3UbXEz5cxMzMrrqdB5IPAJyPiLyLir4F3AO9Lr5RYnh17dvDQ\nCw/ltHmiqpmZ2at6GiCmAr9o34iIu4AAJpezqFqxePVidrbu3LstxJypczKsyMzMrLL0NIgMAnbk\nte0GBpennNqSPz/kTZPexOhhozOqxszMrPL09K4ZAbdI2tmhbRhwk6St7Q0R8c5yFFftvH6ImZlZ\n53oaRP6tQNtt5Sik1uxu3c39q+7PaXMQMTMzy9WjIBIR5/VVIbXmkTWPsHX31py2U6eemlE1ZmZm\nlali7naRdKGk5yVtl/SgpE6fCifpdElLJO2Q9AdJ5xbo81lJyyRtk7RS0nxJ/fKQl0XLF+VsHzn+\nSMaPHN8fH21mZlY1KiKISHo3cC1wGXAM8Bhwp6RxRfpPB/6HZEG1o4HrgO9KekuHPu8Frk6POQM4\nH/g74Kq+Oo+OvH6ImZlZ1yoiiADzgJsj4taIWAZcAGwjCQ+FfAJ4LiIuiYhnIuJG4CfpcdqdBNwb\nET+OiJXprcY/Ao7vu9NItLa1cs+Ke3LaPD/EzMxsX5kHEUmDgdkkVzcAiIgA7iIJE4WcmL7f0Z15\n/e8HZrcP8Ug6FHgb8L/lqby4J9c9ScvOlpy2U6d5foiZmVm+Uh96V07jgHpgbV77WuDwIvtMKtJ/\nf0lDI2JnRDSmQzv3SlL6GTdFxDVlrL2g/Nt2Dz3gUA7Z/5C+/lgzM7OqUwlBpE9IOh34Eskwz2Lg\nMOB6SS9FxD90tu+8efMYPTp34bGGhgYaGhq69dn580PmTpvb7brNzMwqXWNjI42NjTltLS0tRXp3\nrhKCyHqgFZiY1z4RWFNknzVF+m+KiPbF1q4A/j0ivp9uPyVpFHAz0GkQWbBgAbNmzepm+bkiwguZ\nmZlZTSv0y3lTUxOzZ8/u8bEynyMSEbuBJcAZ7W3pUMoZJPM8CnmgY//UW9P2diOAPXl92jocv088\n8/IzrNu6LqfNQcTMzKywSrgiAjCfZOn4JSTDKPNIgsQtAJKuBiZHRPtaITcBF0q6BvgeSSh5F8lk\n1HY/A+ZJegx4CHgdyVWSO9LJsH0i/2rIwfsdzGvGvKavPs7MzKyqVUQQiYjb04mlV5AMsTwKnBkR\nzWmXScCUDv2XS3o7sAD4DPAC8OH0Ft12V5JcAbkSOBhoBu4AvtyX51JoWKYPL8CYmZlVtYoIIgAR\nsRBYWOS9fZaWj4i7SW77LXa89hByZblq7EpEsGhF7oqqnqhqZmZWXOZzRGrJ8leW88KmF3LaPD/E\nzMysOAeRMsoflhk3Yhwzxs3IqBozM7PK5yBSRp4fYmZm1jMOImXkB92ZmZn1jINImby4+UX+uOGP\nOW1zp3uiqpmZWWccRMokf1hm9NDRHDXhqIyqMTMzqw4OImWSH0TmTJ1DfV19RtWYmZlVBweRMvHz\nZczMzHrOQaQM1m9bz1PNT+W0OYiYmZl1zUGkDO5deW/O9ojBI5h9UM+fQGhmZjbQOIiUwaLlucu6\nnzzlZAbXD86oGjMzs+rhIFIGXj/EzMysNA4ivdSyo4VH1zya0+b5IWZmZt3jINJL96+6n7Zo27s9\npH4Ixx98fIYVmZmZVQ8HkV7Kv233hINPYPjg4RlVY2ZmVl0cRHpp0YrciaoeljEzM+s+B5Fe2LZ7\nG79/8fc5bQ4iZmZm3ecg0gsPvvAge9r27N2uVz0nHXJShhWZmZlVFweRXsifHzLroFnsN3S/jKox\nMzOrPg4ivZAfROZOm5tRJWZmZtXJQaREO/fs5IEXHshp8/wQMzOznnEQKdHDLz7Mjj079m4LMWfq\nnAwrMjMzqz4OIiXKH5Y5auJRHDD8gIyqMTMzq04OIiXy82XMzMx6z0GkBHva9nDfyvty2uZO90RV\nMzOznnIQKcGjax5l867NOW2nTj01o2rMzMyql4NICfLnhxx+4OFMHDUxo2rMzMyqV8UEEUkXSnpe\n0nZJD0o6rov+p0taImmHpD9IOrdAn9GSbpT0YtpvmaS/6G2t+UHEt+2amZmVpiKCiKR3A9cClwHH\nAI8Bd0oaV6T/dOB/gN8ARwPXAd+V9JYOfQYDdwFTgXcCrwc+CqzuTa1t0cY9K+/JaXMQMTMzK82g\nrAtIzQNujohbASRdALwdOB/4RoH+nwCei4hL0u1nJM1Jj/PrtO3DwBjgxIhoTdtW9rbQpc1L2bB9\nQ06bV1Q1MzMrTeZXRNIrF7NJrm4AEBFBcjWj2BPkTkzf7+jOvP7vAB4AFkpaI+kJSZdK6tU5L1q+\nKGd7+pjpTBk9pTeHNDMzG7AyDyLAOKAeWJvXvhaYVGSfSUX67y9paLp9KPC3JOd4FnAF8Hng73tT\n7D7rh3hYxszMrGSVMjTTF+pIwsnH0issj0g6BLgYuLKUA0bEvhNVvZCZmZlZySohiKwHWoH8+18n\nAmuK7LOmSP9NEbEz3X4J2JWGkHZPA5MkDYqIPcUKmjdvHqNHj85pa2ho4Ni3HsuaLbkl+YqImZkN\nNI2NjTQ2Nua0tbS0lHSszINIROyWtAQ4A7gDQJLS7euL7PYAyXBLR29N29vdBzTk9TkceKmzEAKw\nYMECZs2atU/7vzb9a872QaMO4rCxh3V2KDMzs5rT0NBAQ0Puj9impiZmz57d42NVwhwRgPnARyV9\nUNIM4CZgBHALgKSrJf1bh/43AYdKukbS4ZI+CbwrPU67fwbGSrpe0uskvR24FPinUotctCJ3oupp\n004jyUxmZmZWisyviABExO3pmiFXkAyxPAqcGRHNaZdJwJQO/ZenwWIB8BngBeDDEXFXhz4vSDoz\n7fMYyfohCyh8O3C3eCEzMzOz8qqIIAIQEQuBhUXeO69A290kt/12dsyHgJPLUd+KV1awomVFTpuD\niJmZWe9UytBMxctfTXXs8LEcOf7IjKoxMzOrDQ4i3VRoWKaud2ujmZmZDXj+SdpN+0xU9fohZmZm\nveYg0g1rtqzhDy//IafN80PMzMx6z0GkG+5ZkTs/ZL8h+3H0pKMzqsbMzKx2OIh0Q/78kFOmnsKg\nuoq54cjMzKxqOYh0Q/6D7uZOm5tRJWZmZrXFQaQLG7Zv4Im1T+S0eX6ImZlZeTiIdOHelfcSvPrc\nvGGDhnHs5GMzrMjMzKx2OIh0IX9+yEmHnMSQ+iEZVWNmZlZbHES64OfLmJmZ9R0HkU5s3rmZppea\ncto8UdXMzKx8HEQ6cf+q+2mN1r3bg+sGc8IhJ2RYkZmZWW1xEOlE/rDMcQcfx4jBIzKqxszMrPY4\niHQif/0QP1/GzMysvBxEiti+ezuLVy/OafNEVTMzs/JyECli8erF7GrdtXe7TnWcMvWUDCsyMzOr\nPQ4iReTPDzlm0jHsP3T/jKoxMzOrTQ4iRSxasShn28MyZmZm5ecgUsDu1t3cv+r+nDYHETMzs/Jz\nEClg2fplbN+zPadtztQ5GVVjZmZWuxxECshfTXXmhJmMGzEuo2rMzMxql4NIAflBxOuHmJmZ9Q0H\nkQIeWfNIzrbnh5iZmfUNB5ECtu7amrN96rRTM6rEzMystjmIdOGwsYcxeb/JWZdhZmZWkxxEujB3\n2tysSzAzM6tZDiJd8PwQMzOzvlMxQUTShZKel7Rd0oOSjuui/+mSlkjaIekPks7tpO97JLVJ+s+e\n1uUgYmZm1ncqIohIejdwLXAZcAzwGHCnpIKLd0iaDvwP8BvgaOA64LuS3lKk7zeBu/Pf68qU/acw\nbfS0nu5mZmZm3VQRQQSYB9wcEbdGxDLgAmAbcH6R/p8AnouISyLimYi4EfhJepy9JNUBtwFfBZ7v\naVGnTTsNST3dzczMzLop8yAiaTAwm+TqBgAREcBdwElFdjsxfb+jOwv0vwxYGxHfL6U2T1Q1MzPr\nW4OyLgAYB9QDa/Pa1wKHF9lnUpH++0saGhE7Jc0BziMZuimJ54eYmZn1rcyviPQFSaOAW4GPRsTG\nUo4xYeQEXn/g68tbmJmZmeWohCsi64FWYGJe+0RgTZF91hTpvym9GjIDmAb8TK9O8qgDkLQLODwi\nis8Z+SXUL6nn7LvP3tvU0NBAQ0ND987IzMyshjU2NtLY2JjT1tLSUtKxlEzHyJakB4GHIuKidFvA\nSuD6iPhmgf5fB86KiKM7tP0QGBMRb5M0FHht3m5XAaOAzwDPRsSeAsedBSzhY3D9+dfz6RM+XaYz\nNDMzq21NTU3Mnj0bYHZENHXVv10lXBEBmA/cImkJsJjk7pcRwC0Akq4GJkdE+1ohNwEXSroG+B5w\nBvAu4G0AEbETWNrxAyS9krwVT3enoLnTPVHVzMysr1VEEImI29M1Q64gGWJ5FDgzIprTLpOAKR36\nL5f0dmAByRWOF4APR0T+nTQlGTV0FDMnzCzHoczMzKwTFRFEACJiIbCwyHvnFWi7m+S23+4ef59j\nFHPMpGOoU03O4zUzM6so/mlbwKyDZmVdgpmZ2YDgIFKAg4iZmVn/cBApYMa4GVmXYGZmNiA4iBQw\nqK5ips6YmZnVNAcRMzMzy4yDiJmZmWXGQcTMzMwy4yBiZmZmmXEQMTMzs8w4iJiZmVlmHETMzMws\nMw4iZmZmlhkHETMzM8uMg4iZmZllxkHEzMzMMuMgYmZmZplxEDEzM7PMOIiYmZlZZhxEzMzMLDMO\nImZmZpYZBxEzMzPLjIOImZmZZcZBxMzMzDLjIGJmZmaZcRAxMzOzzDiImJmZWWYcRMzMzCwzDiJm\nZmaWmYoJIpIulPS8pO2SHpR0XBf9T5e0RNIOSX+QdG7e+x+RdLekDenr110ds9Y0NjZmXUJZ+Xwq\nVy2dC/h8KlktnQvU3vmUoiKCiKR3A9cClwHHAI8Bd0oaV6T/dOB/gN8ARwPXAd+V9JYO3eYCPwRO\nB04EVgG/knRQn5xEBaq1/8B9PpWrls4FfD6VrJbOBWrvfEpREUEEmAfcHBG3RsQy4AJgG3B+kf6f\nAJ6LiEsi4pmIuBH4SXocACLiAxFxU0Q8HhF/AD5Ccr5n9OmZmJmZWbdlHkQkDQZmk1zdACAiArgL\nOKnIbiem73d0Zyf9AUYCg4ENJRdrZmZmZZV5EAHGAfXA2rz2tcCkIvtMKtJ/f0lDi+xzDbCafQOM\nmZmZZWRQ1gX0B0lfBP4OmBsRuzrpOgzg6aef7pe6+lpLSwtNTU1Zl1E2Pp/KVUvnAj6fSlZL5wK1\ndT4dfnYO68l+SkZBspMOzWwD/iYi7ujQfgswOiLOKbDPImBJRHyuQ9uHgAURcUBe34uBLwFnRMQj\nXdTyXuAHpZ+NmZnZgPe+iPhhdztnfkUkInZLWkIyifQOAElKt68vstsDwFl5bW9N2/eSdAlwKfDW\nrkJI6k7gfcByYEc3T8HMzMySKyHTSX6WdlvmV0QAJP0dcAvJ3TKLSe5+eRcwIyKaJV0NTI6Ic9P+\n04EngIXA90hCy7eBt0XEXWmfLwBfAxqA+zt83JaI2Nr3Z2VmZmZdyfyKCEBE3J6uGXIFMBF4FDgz\nIprTLpOAKR36L5f0dmAB8BngBeDD7SEkdQHJXTI/yfu4r6WfY2ZmZhmriCsiZmZmNjBVwu27ZmZm\nNkA5iJiZmVlmHERSPX3oXqWSdKqkOyStltQm6a+yrqlUki6VtFjSJklrJf2XpNdnXVepJF0g6TFJ\nLenrfkl/kXVd5SDpi+l/b/OzrqUUki5L6+/4Wpp1Xb0habKkf5e0XtK29L+9WVnXVYr0e3P+v0+b\npBuyrq2nJNVJulLSc+m/yx8lfTnrunpD0ihJ35a0PD2neyUd2939HUTo+UP3KtxIksm+nwSqfQLQ\nqcANwAnAn5NMPv6VpOGZVlW6VcAXgFkkjzX4P+C/JR2RaVW9lIb2j5H8f1PNniSZLD8pfc3JtpzS\nSRoD3AfsBM4EjgA+D2zMsq5eOJZX/10mAW8h+f52e5ZFleiLwMdJvkfPAC4BLpH0qUyr6p1/Jbl7\n9X3ATODXwF3dfcisJ6sCkh4EHoqIi9JtkfzQuD4ivpFpcb0gqQ34644LxVWzNBiuA06LiHuzrqcc\nJL0MXBwR38+6llJIGgUsIXkQ5VeARzouNFgtJF0GnB0RVXnFIJ+krwMnRcTcrGvpC5Lal2uouiuk\nkn4GrImIj3Zo+wmwLSI+mF1lpZE0DNgMvCMiftmh/WHg5xHx1a6OMeCviJT40D3LxhiS34Kq/sGF\n6eXZ9wAjyFuIr8rcCPwsIv4v60LK4HXpkOafJN0maUrXu1SsdwAPS7o9HdZskvSRrIsqh/R79vtI\nfguvRvcDZ0h6HYCko4FTgJ9nWlXpBpE8L25nXvt2unlVsSLWEclYZw/dO7z/y7FC0qtU3wbujYiq\nHbuXNJMkeLT/FnFORCzLtqrSpEHqTSSXzavdg8CHgGeAg4DLgbslzazSBRAPJblKdS1wFXA8cL2k\nnRHx75lW1nvnAKOBf8u6kBJ9HdgfWCapleSCwN9HxI+yLas0EbFF0gPAVyQtI/nZ+V6SX+Sf7c4x\nHESsWiwEjiT5zaGaLQOOJvlG+i7gVkmnVVsYkXQISTD884jYnXU9vRURHZekflLSYmAFycMyq3HY\nrA5YHBFfSbcfS0PwBUC1B5HzgV9ExJqsCynRu0l+UL8HWEoS5q+T9GIVh8T3k6xyvhrYAzQBPyQZ\nbeiSgwisB1pJJql1NBGo1v/Qa4qkfwL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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1136e4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from wmf import *\n",
    "max_iteration = 10\n",
    "alpha=40\n",
    "model = wmf(train_list=train_list, \n",
    "            test_list=test_list, \n",
    "            N=N, \n",
    "            M=M,\n",
    "            K=K,\n",
    "            alpha=alpha,\n",
    "            lamda_regularizer=lamda_regularizer, \n",
    "            max_iteration=max_iteration)\n",
    "P, Q, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,0][-1],records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,2],name='Recall')\n",
    "figure(values_list=records_array[:,3],name='Precision')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. 带偏置的SVD（BiasSVD）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " loss:46763.4749,mae:0.8175,rmse:1.0195,recall:0.0647,precision:0.1372\n",
      " step:10 \n",
      " loss:47389.7184,mae:0.7510,rmse:0.8992,recall:0.0391,precision:0.0828\n",
      " step:20 \n",
      " loss:47709.3466,mae:0.7465,rmse:0.8903,recall:0.0316,precision:0.0669\n",
      " step:30 \n",
      " loss:47387.3729,mae:0.7417,rmse:0.8799,recall:0.0265,precision:0.0561\n",
      " step:40 \n",
      " loss:46674.2320,mae:0.7344,rmse:0.8639,recall:0.0307,precision:0.0650\n",
      " step:50 \n",
      " loss:45928.8626,mae:0.7288,rmse:0.8521,recall:0.0336,precision:0.0714\n",
      " step:60 \n",
      " loss:45228.4016,mae:0.7249,rmse:0.8445,recall:0.0339,precision:0.0719\n",
      " step:70 \n",
      " loss:44611.5566,mae:0.7225,rmse:0.8401,recall:0.0331,precision:0.0702\n",
      " step:80 \n",
      " loss:44106.0715,mae:0.7211,rmse:0.8381,recall:0.0312,precision:0.0662\n",
      " step:90 \n",
      " loss:43706.7132,mae:0.7205,rmse:0.8376,recall:0.0296,precision:0.0628\n",
      " end. \n",
      " loss:43422.6423,mae:0.7203,rmse:0.8379,recall:0.0276,precision:0.0585\n",
      "MAE:0.7203;RMSE:0.8379;Recall:0.0276;Precision:0.0585\n"
     ]
    },
    {
     "data": {
      "image/png": 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OBJ1ukaOpKolGnS7oxGfXfUZcTJwn/u/F/+bvU/+uQkdEopaKnAg63YXHmqqS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\nSCSW2xyriNFUlUju1a56O6b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DFTkiIpIt0ndfzewzkyolqoS1v7LoFS557xLW/rbWh+wk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\n81tYcNsCFt2+iB65Pfha5a8VWz9j1Qx+9NyPqD2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      "text/plain": [
       "<matplotlib.figure.Figure at 0xa036c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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7AfjEOfeycy7fOTcN+Fegb52EhpXismK27dtWj68lIiIihyruYcXMkoFsYHplm/OGL6bh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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1235b240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from biassvd import *\n",
    "max_iteration = 100\n",
    "model = biassvd(train_list=train_list, \n",
    "                test_list=test_list, \n",
    "                N=N, \n",
    "                M=M,\n",
    "                K=K,\n",
    "                learning_rate=learning_rate, \n",
    "                lamda_regularizer=lamda_regularizer, \n",
    "                max_iteration=max_iteration)\n",
    "P, Q, bu, bi, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1],records_array[:,4][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,0],name='loss')\n",
    "figure(values_list=records_array[:,1],name='MAE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. SVD++"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " step:0 \n",
      " loss:114770.6618,mae:0.8175,rmse:1.0198,recall:0.0652,precision:0.1383\n",
      " step:10 \n",
      " loss:47597.8449,mae:0.7509,rmse:0.8988,recall:0.0391,precision:0.0828\n",
      " step:20 \n",
      " loss:47830.7927,mae:0.7454,rmse:0.8879,recall:0.0323,precision:0.0685\n",
      " step:30 \n",
      " loss:47572.2334,mae:0.7376,rmse:0.8714,recall:0.0295,precision:0.0626\n",
      " step:40 \n",
      " loss:46897.3534,mae:0.7289,rmse:0.8531,recall:0.0333,precision:0.0705\n",
      " step:50 \n",
      " loss:46207.0482,mae:0.7238,rmse:0.8422,recall:0.0341,precision:0.0723\n",
      " step:60 \n",
      " loss:45599.5553,mae:0.7205,rmse:0.8358,recall:0.0336,precision:0.0714\n",
      " step:70 \n",
      " loss:45082.6841,mae:0.7185,rmse:0.8321,recall:0.0322,precision:0.0683\n",
      " step:80 \n",
      " loss:44661.2057,mae:0.7172,rmse:0.8303,recall:0.0311,precision:0.0660\n",
      " step:90 \n",
      " loss:44327.7244,mae:0.7165,rmse:0.8296,recall:0.0288,precision:0.0610\n",
      " end. \n",
      " loss:44090.3840,mae:0.7162,rmse:0.8297,recall:0.0276,precision:0.0585\n",
      "MAE:0.7162;RMSE:0.8297;Recall:0.0276;Precision:0.0585\n"
     ]
    },
    {
     "data": {
      "image/png": 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xs6nNBuAFFc3MzMo33KGxg4D9IuLV2oaIeEXSl4AHRuTMNnMeGjMzMyvfcHuE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\n9e15kHo/NYPiIDRK0r+WF5E9tBXoGb6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      "text/plain": [
       "<matplotlib.figure.Figure at 0x122af7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WoujfvnJYWZ29OkGViIiING0KK1HozIqIiEhyUFiJol+HfpXeK6yIiIgkhsJKFFXPrGzZ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\ndgT3adoPjAUGAT8muGlleR8d99iaDHw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x122af860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from svdplus import *\n",
    "model = svdplus(train_list=train_list, \n",
    "                test_list=test_list, \n",
    "                N=N, \n",
    "                M=M,\n",
    "                K=K,\n",
    "                learning_rate=learning_rate, \n",
    "                lamda_regularizer=lamda_regularizer, \n",
    "                max_iteration=max_iteration)\n",
    "P, Q, Y, bu, bi, records_array = model.train()\n",
    "print('MAE:%.4f;RMSE:%.4f;Recall:%.4f;Precision:%.4f'\n",
    "      %(records_array[:,1][-1],records_array[:,2][-1],records_array[:,3][-1],records_array[:,4][-1]))\n",
    "\n",
    "figure(values_list=records_array[:,0],name='loss')\n",
    "figure(values_list=records_array[:,1],name='MAE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8. PureSVD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mae:2.3452,rmse:6.8323,recall:0.1618,precision:0.3432\n"
     ]
    }
   ],
   "source": [
    "from puresvd import *\n",
    "R_score = puresvd(R=train_mat, k=K)\n",
    "mae, rmse, recall, precision = evaluation(pred_mat=R_score, train_mat=train_mat, test_mat=test_mat)\n",
    "print('mae:%.4f,rmse:%.4f,recall:%.4f,precision:%.4f'%(mae,rmse,recall,precision))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
   "name": "conda-root-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
